Newform orbit 945.2.cc.a

• Label: 945.2.cc.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.cc
• Analytic conductor: $7.546$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.54586299101\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 8 q^{7}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
82.1	−2.70653	+	0.725214i		0		5.06734	−	2.92563i	−0.582598	−	2.15884i		0		−1.87525	−	1.86640i	−7.63059	+	7.63059i		0		3.14244	+	5.42046i
82.2	−2.42255	+	0.649122i		0		3.71536	−	2.14507i	−0.767700	+	2.10015i		0		2.52094	+	0.803028i	−4.06139	+	4.06139i		0		0.496542	−	5.58606i
82.3	−2.36642	+	0.634081i		0		3.46585	−	2.00101i	−2.22777	+	0.192431i		0		−0.800970	+	2.52160i	−3.46818	+	3.46818i		0		5.14984	−	1.86796i
82.4	−2.31911	+	0.621403i		0		3.26006	−	1.88220i	1.91020	+	1.16238i		0		1.84774	−	1.89364i	−2.99543	+	2.99543i		0		−5.15227	−	1.50867i
82.5	−2.10293	+	0.563479i		0		2.37276	−	1.36992i	−0.789671	−	2.09199i		0		2.63835	−	0.197733i	−1.13894	+	1.13894i		0		2.83942	+	3.95435i
82.6	−1.97779	+	0.529947i		0		1.89875	−	1.09625i	1.71761	+	1.43172i		0		−2.61323	−	0.413543i	−0.278697	+	0.278697i		0		−4.15581	−	1.92139i
82.7	−1.78707	+	0.478845i		0		1.23228	−	0.711459i	1.42046	−	1.72693i		0		−2.30923	−	1.29130i	0.754954	−	0.754954i		0		−1.71153	+	3.76633i
82.8	−1.54962	+	0.415220i		0		0.496873	−	0.286870i	−2.23119	+	0.147569i		0		0.0784759	−	2.64459i	1.61795	−	1.61795i		0		3.39624	−	1.15511i
82.9	−1.39331	+	0.373336i		0		0.0698789	−	0.0403446i	0.709966	+	2.12037i		0		−1.34070	+	2.28090i	1.95764	−	1.95764i		0		−1.78081	−	2.68927i
82.10	−1.34647	+	0.360785i		0		−0.0492386	+	0.0284279i	−1.34313	−	1.78774i		0		−0.423172	+	2.61169i	2.02741	−	2.02741i		0		2.45347	+	1.92256i
82.11	−1.17569	+	0.315026i		0		−0.449041	+	0.259254i	−1.79423	+	1.33444i		0		−1.33548	−	2.28397i	2.16759	−	2.16759i		0		1.68908	−	2.13412i
82.12	−0.772202	+	0.206911i		0		−1.17857	+	0.680446i	2.09761	+	0.774613i		0		2.11780	−	1.58585i	1.89988	−	1.89988i		0		−1.78006	−	0.164139i
82.13	−0.678049	+	0.181683i		0		−1.30531	+	0.753621i	1.99409	−	1.01174i		0		1.52686	+	2.16071i	1.74088	−	1.74088i		0		−1.16827	+	1.04830i
82.14	−0.646431	+	0.173211i		0		−1.34418	+	0.776063i	−0.270716	+	2.21962i		0		2.23956	+	1.40868i	1.68094	−	1.68094i		0		−0.209463	−	1.48172i
82.15	−0.240990	+	0.0645732i		0		−1.67814	+	0.968877i	1.83527	−	1.27741i		0		−2.64502	+	0.0621414i	0.694688	−	0.694688i		0		−0.359797	+	0.426352i
82.16	−0.121772	+	0.0326286i		0		−1.71829	+	0.992054i	−0.668137	−	2.13391i		0		1.10538	−	2.40378i	0.355155	−	0.355155i		0		0.150987	+	0.238050i
82.17	0.121772	−	0.0326286i		0		−1.71829	+	0.992054i	0.668137	+	2.13391i		0		1.10538	−	2.40378i	−0.355155	+	0.355155i		0		0.150987	+	0.238050i
82.18	0.240990	−	0.0645732i		0		−1.67814	+	0.968877i	−1.83527	+	1.27741i		0		−2.64502	+	0.0621414i	−0.694688	+	0.694688i		0		−0.359797	+	0.426352i
82.19	0.646431	−	0.173211i		0		−1.34418	+	0.776063i	0.270716	−	2.21962i		0		2.23956	+	1.40868i	−1.68094	+	1.68094i		0		−0.209463	−	1.48172i
82.20	0.678049	−	0.181683i		0		−1.30531	+	0.753621i	−1.99409	+	1.01174i		0		1.52686	+	2.16071i	−1.74088	+	1.74088i		0		−1.16827	+	1.04830i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
5.c	odd	4	1	inner
7.d	odd	6	1	inner
15.e	even	4	1	inner
21.g	even	6	1	inner
35.k	even	12	1	inner
105.w	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	945.2.cc.a	✓	128
3.b	odd	2	1	inner	945.2.cc.a	✓	128
5.c	odd	4	1	inner	945.2.cc.a	✓	128
7.d	odd	6	1	inner	945.2.cc.a	✓	128
15.e	even	4	1	inner	945.2.cc.a	✓	128
21.g	even	6	1	inner	945.2.cc.a	✓	128
35.k	even	12	1	inner	945.2.cc.a	✓	128
105.w	odd	12	1	inner	945.2.cc.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
945.2.cc.a	✓	128	1.a	even	1	1	trivial
945.2.cc.a	✓	128	3.b	odd	2	1	inner
945.2.cc.a	✓	128	5.c	odd	4	1	inner
945.2.cc.a	✓	128	7.d	odd	6	1	inner
945.2.cc.a	✓	128	15.e	even	4	1	inner
945.2.cc.a	✓	128	21.g	even	6	1	inner
945.2.cc.a	✓	128	35.k	even	12	1	inner
945.2.cc.a	✓	128	105.w	odd	12	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^128 - 240*T2^124 + 33200*T2^120 - 3094388*T2^116 + 215934052*T2^112 - 11706983034*T2^108 + 508636416650*T2^104 - 17931073382864*T2^100 + 518795720349950*T2^96 - 12347782568001984*T2^92 + 242506514979718199*T2^88 - 3916842860942477632*T2^84 + 51960322737559785395*T2^80 - 562021285997238770430*T2^76 + 4942945548546777949942*T2^72 - 35005650281733002062586*T2^68 + 199315322982457169542817*T2^64 - 900936708430437804632216*T2^60 + 3220058057316065157336300*T2^56 - 8879749063212591724119794*T2^52 + 18636085053389331411389167*T2^48 - 28029542447772858859658354*T2^44 + 29559892268756678251181811*T2^40 - 18080190518811461220153622*T2^36 + 7870530532642169519304809*T2^32 - 2209675392774206635518896*T2^28 + 448832139716237977117136*T2^24 - 54626687887361098617032*T2^20 + 4303341788441251748396*T2^16 - 17681529079867841600*T2^12 + 65692274347860000*T2^8 - 16523787500000*T2^4 + 3906250000